Abstract:
The paper is devoted to the theory of “traces” in the spaces
$$
W^\infty\{a_\alpha,p_\alpha\}(G)=\{u(x)\in C^\infty(G):\quad\sum_{|\alpha|=0}^{\infty}a_\alpha\|D^\alpha u\|_{p_\alpha}^{p_\alpha}<\infty\}
$$
and to the inhomogeneous Dirichlet problem for elliptic equations of infinite order. A trace criterion is established, simple sufficient trace conditions are adduced, and the correctness of the indicated Dirichlet problem is proved on the basis of the results obtained.
Bibliography: 6 titles.